Systems and methods for reduced off-resonance blurring in spiral imaging

ABSTRACT

Systems, methods of reducing off-resonance blurring in acquired magnetic resonance imaging data. The method includes acquiring a first set of spiral interleaf data for each of one or more spiral-in/out interleaves by performing a first sampling each of one or more locations in k-space along a first redundant spiral-in/out trajectory, and acquiring a second set of spiral interleaf data for each of the one or more spiral-in/out interleaves by performing a second sampling of each of the one or more locations in the k-space along a second redundant spiral-in/out trajectory, wherein the second redundant spiral-in/out trajectory corresponds to a time-reversed trajectory of the first redundant spiral-in/out trajectory. The method may yet further include combining the first set of spiral interleaf data and the second set of spiral interleaf data with an averaging operation such as to reduce artifacts.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims priority to and benefit under 35 U.S.C. §119(e)of U.S. Provisional Patent Application Ser. No. 61/636,551, entitled“Simple Acquisition Strategy to Avoid Off-Resonance Blurring in SpiralImaging”, filed Apr. 20, 2012, which is hereby incorporated by referenceas if fully set forth below.

Some references, which may include patents, patent applications, andvarious publications, are cited in a reference list and discussed in thedisclosure provided herein. The citation and/or discussion of suchreferences is provided merely to clarify the description of the presentdisclosure and is not an admission that any such reference is “priorart” to any aspects of the present disclosure described herein. Allreferences cited and discussed in this specification are incorporatedherein by reference in their entireties and to the same extent as ifeach reference was individually incorporated by reference. In terms ofnotation, hereinafter, “[n]” represents the nth reference cited in thereference list. For example, [4] represents the 4th reference cited inthe reference list, namely, Noll et al., “A homogeneity correctionmethod for magnetic resonance imaging with time-varying gradients.” IEEET Med Imaging 10:629-637 (1991).

STATEMENT OF RIGHTS UNDER FEDERALLY-SPONSORED RESEARCH

The invention was made in part with U.S. Government support under GrantHL079110, awarded by the National Institute of Health. The U.S.Government has certain rights in the invention.

BACKGROUND

Spiral k-space trajectories offer many advantages over traditionalrectilinear acquisitions, including improved acquisition efficiency,less stringent hardware requirements, and natural resilience to flow andmotion. However, a major hurdle to wide-spread adoption of spiraltrajectories has been their poor off-resonance performance. Efforts tocorrect or at least mitigate the resultant blurring have resulted inlengthy algorithms often requiring several seconds to reconstruct asingle image. It is with respect to these and other considerations thatthe various embodiments described below are presented.

SUMMARY

The present disclosure relates generally to magnetic resonance imaging(MRI) and, more particularly, systems, methods, and computer programproducts for reduced off-resonance blurring in spiral imaging. In oneaspect, the present disclosure relates to a method of acquiring magneticresonance imaging (MRI) data associated with an area of interest of asubject. In one example embodiment, the method includes acquiring afirst set of spiral interleaf data for each of one or more spiral-in/outinterleaves by performing a first sampling each of one or more locationsin k-space along a first redundant spiral-in/out trajectory. The methodmay further include acquiring a second set of spiral interleaf data foreach of the one or more spiral-in/out interleaves by performing a secondsampling of each of the one or more locations in the k-space along asecond redundant spiral-in/out trajectory. The second redundantspiral-in/out trajectory may correspond to a time-reversed trajectory ofthe first redundant spiral-in/out trajectory. The method may yet furtherinclude combining the first set of spiral interleaf data and the secondset of spiral interleaf data with an averaging operation such as toreduce artifacts.

In another aspect, the present disclosure relates to a system. In oneexample embodiment, the system includes a magnetic resonance imaging(MRI) device, one or more processors, and at least one memory device incommunication with the MRI device. The memory device storescomputer-readable instructions that, when executed by the one or moreprocessors, cause the system to perform functions that include acquiringa first set of spiral interleaf data, by the MRI device, for each of oneor more spiral-in/out interleaves by performing a first sampling each ofone or more locations in k-space along a first redundant spiral-in/outtrajectory. The method may further include acquiring a second set ofspiral interleaf data for each of the one or more spiral-in/outinterleaves by performing a second sampling of each of the one or morelocations in the k-space along a second redundant spiral-in/outtrajectory. The second redundant spiral-in/out trajectory may correspondto a time-reversed trajectory of the first redundant spiral-in/outtrajectory. The functions may yet further include combining, by the oneor more processors, the first set of spiral interleaf data and thesecond set of spiral interleaf data with an averaging operation such asto reduce artifacts.

In yet another aspect, the present disclosure relates to acomputer-readable storage medium. In one example embodiment, thecomputer-readable medium has stored computer-executable instructionsthat, when executed by one or more processors, cause a computer toperform functions that include acquiring a first set of spiral interleafdata for each of one or more spiral-in/out interleaves by performing afirst sampling each of one or more locations in k-space along a firstredundant spiral-in/out trajectory. The functions may further includeacquiring a second set of spiral interleaf data for each of the one ormore spiral-in/out interleaves by performing a second sampling of eachof the one or more locations in the k-space along a second redundantspiral-in/out trajectory. The second redundant spiral-in/out trajectorymay correspond to a time-reversed trajectory of the first redundantspiral-in/out trajectory. The functions may yet further includecombining the first set of spiral interleaf data and the second set ofspiral interleaf data with an averaging operation such as to removeartifacts.

Other aspects and features according to the present disclosure willbecome apparent to those of ordinary skill in the art, upon reviewingthe following detailed description in conjunction with the accompanyingfigures.

BRIEF DESCRIPTION OF THE DRAWINGS

The patent or application filed contains at least one drawing executedin color. Copies of this patent or patent application publication withcolor drawing(s) will be provided by the Office upon request and paymentof the necessary fee.

FIG. 1 is a system diagram illustrating an operating environment capableof implementing aspects of the present disclosure in accordance with oneor more example embodiments.

FIG. 2 is a computer architecture diagram showing illustrative computerhardware architecture for a computing system capable of implementingaspects of the present disclosure in accordance with one or more exampleembodiments.

FIG. 3 is a flow chart illustrating operations of a method for acquiringmagnetic resonance imaging (MRI) data, in accordance with one exampleembodiment of the present disclosure.

FIGS. 4A-B illustrate spiral-out and spiral-in/out read gradients,respectively, in accordance with one example embodiment of the presentdisclosure.

FIGS. 4C-D illustrate k-space trajectories for spiral out andspiral-in/out trajectories, respectively, in accordance with one exampleembodiment of the present disclosure.

FIGS. 5A-B illustrate spiral in arms and spiral out arms fornon-redundant and redundant spiral-in/out trajectories, respectively, inaccordance with one example embodiment of the present disclosure. Eachof these trajectories is spiral-in/out, but for ease of visualization,blue lines represent spiral-in arms of the trajectories; red representsspiral-out.

FIGS. 6A-B illustrate point-spread-functions (PSF) for spiral-out,non-redundant spiral-in/out, and redundant spiral-in/out trajectoryvariations, in accordance with one example embodiment of the presentdisclosure. Center line of 2D PSF is shown for each trajectoryvariation. Numbers in parentheses are FWTM values for each trajectory.In FIG. 6A, on-resonance, PSFs are nearly indistinguishable. In FIG. 6B,50 Hz off-resonance (0.5 cycles of phase accrued by the end of thereadout), the spiral-out trajectory shows expected broadening; Thenon-redundant spiral-in/out shows narrow main lobe along with verypronounced side lobe “rings”; and the redundant spiral-in/out removesthese rings, leaving the narrow main lobe.

FIGS. 7A-C illustrate normalized modulation transfer functions (MTFs) ofspiral-in/out trajectories, in accordance with one example embodiment ofthe present disclosure. The MTFs were normalized to on-resonance (0cycles) case. FIG. 7A shows center-frequency offset. Until ˜0.5 cyclesof phase are accrued, the cosine function never reaches its first zero,resulting in a relatively benign amplitude modulation in k-space;however, important frequencies are lost as the amount of off-resonanceincreases. FIG. 7B shows off-resonance due to concomitant fields. MTFsfor off-resonance due to concomitant fields show good performance can beexpected up to about 1 cycle of accrued phase. FIG. 7C shows the effectof decay during the readout. Differing amounts of T₂ decay weresimulated with 0.5 cycles of off-resonance phase accrual. Severe shapingof the MTF is only seen when the T2 time constant approaches the readoutlength (10 ms)

FIG. 8 illustrates reconstructions of numerical phantom inverse-griddedwith spiral-out, linear ordering non-redundant, interleaved orderingredundant, and redundant trajectories, in accordance with one exampleembodiment of the present disclosure. Two non-redundant (NR)trajectories were included in this simulation. For linear ordering (LO),all spiral-in arms were clustered (see FIG. 5A). In interleaved ordering(IO) (see FIG. 5B), each spiral-in arm is surrounded by a spiral-outarm. Difference images are versus ideal (On Resonance, No Decay) imageand color-inverted for ease of visualization. The row 2 difference isx5; all others are x1. The number of interleaves=15 for spiral-out andboth non-redundant trajectories, 30 for redundant. The numbers in bottomright of the difference images indicate RMSE versus ideal image.

FIG. 9 illustrates phantom images at various amounts of off-resonancefor spiral out and spiral-in/out trajectories, in accordance with oneexample embodiment of the present disclosure. The top row showsspiral-out, the bottom row shows spiral-in/out. No off-resonancecorrection was applied. Images were acquired with a 10 ms readout,resulting in cycles of phase accumulated at the end of the readout: 0Hz=0 cycles, 20 Hz=0.2 cycles, 40 Hz=0.4 cycles, 80 Hz=0.8 cycles, 160Hz=1.6 cycles

FIGS. 10A-D illustrate trajectory performance in the presence ofconcomitant fields for spiral-out at isocenter, spiral-in/out atisocenter, spiral-out off center, and spiral-in/out off center. FIG. 10Ashows spiral-out at isocenter. FIG. 10B shows spiral-in/out atisocenter. FIG. 10C shows spiral-out off-center. Note the blurring nearthe top of the phantom due to concomitant fields. FIG. 10D showsspiral-in/out off-center. The blurring due to concomitant fields isreduced.

FIG. 11A-C illustrate a slice from a 3D stack-of-spiral sequence forspiral-out, redundant spiral-in/out, and combined redundantspiral-in/out acquisitions, respectively.

FIGS. 12A-B illustrate spiral out and redundant spiral-in/outacquisitions, respectively, in a volunteer with no off-resonancecorrection applied. In FIG. 12A, significant blurring may be observed inareas with poor homogeneity (insets). In FIG. 12B, improvedoff-resonance performance is obtained with little to no increase in scantime.

FIGS. 13A-B illustrate spiral out and redundant spiral-in/outacquisitions, respectively, for non-contrast MRA in a volunteer with nooff-resonance correction applied. In FIG. 12A, blurring may be observednear the femoral bifurcation as well as more distally. In FIG. 12B,improved sharpness of the femoral artery may be observed.

DETAILED DESCRIPTION

Embodiments of the disclosed technology relate generally to magneticresonance imaging (MRI) and, more particularly, to systems and methodsfor reduced off resonance blurring in spiral imaging. Some embodimentsof the disclosed technology may use a self-correcting spiral trajectorythat may reduce much of the well-known spiral blurring during dataacquisition. In comparison with a traditional spiral-out trajectory, thedisclosed spiral-in/out trajectory may provide improved off-resonanceperformance. In an example embodiment, by combining two spiral-in/outacquisitions (e.g., one rotated 180° in k-space compared to the other)multi-shot spiral-in/out artifacts may be reduced significantly.

Although example embodiments of the present disclosure are explained indetail, it is to be understood that other embodiments are contemplated.Accordingly, it is not intended that the present disclosure be limitedin its scope to the details of construction and arrangement ofcomponents set forth in the following description or illustrated in thedrawings. The present disclosure is capable of other embodiments and ofbeing practiced or carried out in various ways.

It must also be noted that, as used in the specification and theappended claims, the singular forms “a,” “an” and “the” include pluralreferents unless the context clearly dictates otherwise.

In describing example embodiments, terminology will be resorted to forthe sake of clarity. It is intended that each term contemplates itsbroadest meaning as understood by those skilled in the art and includesall technical equivalents that operate in a similar manner to accomplisha similar purpose.

By “comprising” or “containing” or “including” is meant that at leastthe named compound, element, particle, or method step is present in thecomposition or article or method, but does not exclude the presence ofother compounds, materials, particles, method steps, even if the othersuch compounds, material, particles, method steps have the same functionas what is named.

Ranges may be expressed herein as from “about” or “approximately” oneparticular value and/or to “about” or “approximately” another particularvalue. When such a range is expressed, another embodiment includes fromthe one particular value and/or to the other particular value. As usedherein, “about” means within 20 percent or closer of a given value orrange.

As discussed herein, a “subject” or “patient” may be a human or anyanimal. It should be appreciated that an animal may be a variety of anyapplicable type, including, but not limited thereto, mammal,veterinarian animal, livestock animal or pet type animal, etc. As anexample, the animal may be a laboratory animal specifically selected tohave certain characteristics similar to a human (e.g. rat, dog, pig,monkey), etc. It should be appreciated that the subject may be anyapplicable human patient, for example.

It is also to be understood that the mention of one or more steps of amethod does not preclude the presence of additional method steps orintervening method steps between those steps expressly identified. Stepsof a method may be performed in a different order than those describedherein. Similarly, it is also to be understood that the mention of oneor more components in a device or system does not preclude the presenceof additional components or intervening components between thosecomponents expressly identified.

The following detailed description is directed to systems and methodsfor reduced off-resonance blurring in spiral imaging In the followingdetailed description, references are made to the accompanying drawingsthat form a part hereof and that show, by way of illustration, specificembodiments or examples. In referring to the drawings, like numeralsrepresent like elements throughout the several figures.

FIG. 1 is a system diagram illustrating an operating environment capableof implementing aspects of the present disclosure in accordance with oneor more example embodiments. Embodiments may be implemented on acommercial MRI system. FIG. 1 illustrates an example of such an MRIsystem 100, including a data acquisition and display computer 150coupled to an operator console 110, a MRI real-time control sequencer152, and a MRI subsystem 154. The MRI subsystem 154 may include XYZmagnetic gradient coils and associated amplifiers 168, a static Z-axismagnet 169, a digital RF transmitter 162, a digital RF receiver 160, atransmit/receive switch 164, and RF coil(s) 166. The MRI subsystem 154may be controlled in real time by control sequencer 152 to generatemagnetic and radio frequency fields that stimulate magnetic resonancephenomena in a living subject, patient P, to be imaged. Acontrast-enhanced image of an area of interest A of the patient P may beshown on display 158.

The area of interest A corresponds to a region associated with one ormore physiological activities in patient P. The area of interest shownin the example embodiment of FIG. 1 corresponds to a chest region ofpatient P. It will be appreciated that area of interest A canadditionally or alternatively correspond to, but is not limited to, oneor more of a brain region, cardiac region, and upper or lower limbregions of the patient P. Display 158 may be implemented through avariety of output interfaces, including a monitor, printer, or datastorage. It will be appreciated that any number and type ofcomputer-based tomography imaging systems or components, includingvarious types of magnetic resonance imaging systems, may be used topractice aspects of the present disclosure, and the disclosure shouldnot be limited to the type of MRI subsystem shown in FIG. 1.

FIG. 2 is a computer architecture diagram showing illustrative computerhardware architecture for a computing system capable of implementingaspects of the present disclosure in accordance with one or more exampleembodiments described herein. An example implementation of the computer200 may include the data acquisition and display computer 150 of FIG. 1.The computer 200 includes a processing unit 202 (“CPU”), a system memory204, and a system bus 206 that couples the memory 204 to the CPU 202.The computer 200 further includes a mass storage device 212 for storingprogram modules 214. The program modules 214 may be operable to performvarious operations discussed below with respect to FIGS. 3-13 and mayinclude a web server application 236 and an imaging application 218. Thecomputer can include a data store 238 for storing data that may includeimaging-related data 240 such as image acquisition data, and a modelingdata store 242 for storing image modeling data, or other various typesof data utilized in practicing aspects of the present disclosure.

The mass storage device 212 is connected to the CPU 202 through a massstorage controller (not shown) connected to the bus 206. The massstorage device 212 and its associated computer-storage media providenon-volatile storage for the computer 200. Although the description ofcomputer-storage media contained herein refers to a mass storage device,such as a hard disk or CD-ROM drive, it should be appreciated by thoseskilled in the art that computer-storage media can be any availablecomputer storage media that can be accessed by the computer 200.

By way of example, and not limitation, computer-storage media mayinclude volatile and non-volatile, removable and non-removable mediaimplemented in any method or technology for storage of information suchas computer-storage instructions, data structures, program modules, orother data. For example, computer storage media includes, but is notlimited to, RAM, ROM, EPROM, EEPROM, flash memory or other solid statememory technology, CD-ROM, digital versatile disks (“DVD”), HD-DVD,BLU-RAY, or other optical storage, magnetic cassettes, magnetic tape,magnetic disk storage or other magnetic storage devices, or any othermedium which can be used to store the desired information and which canbe accessed by the computer 200.

According to various embodiments, the computer 200 may operate in anetworked environment using logical connections to remote computersthrough a network 216. The computer 200 may connect to the network 216through a network interface unit 210 connected to the bus 206. It shouldbe appreciated that the network interface unit 210 may also be utilizedto connect to other types of networks and remote computer systems. Thecomputer 200 may also include an input/output controller 208 forreceiving and processing input from a number of input devices. The bus206 may enable the processing unit 202 to read code and/or data to/fromthe mass storage device 212 or other computer-storage media. Thecomputer-storage media may represent apparatus in the form of storageelements that are implemented using any suitable technology, includingbut not limited to semiconductors, magnetic materials, optics, or thelike.

The computer-storage media may represent memory components, whethercharacterized as RAM, ROM, flash, or other types of technology. Thecomputer-storage media may also represent secondary storage, whetherimplemented as hard drives or otherwise. Hard drive implementations maybe characterized as solid state, or may include rotating media storingmagnetically-encoded information. The program modules 214, which includethe imaging application 218, may include software instructions that,when loaded into the processing unit 202 and executed, cause thecomputer 200 to provide functions for accelerated arterial spin labeling(ASL) using compressed sensing, according to aspects of the presentdisclosure described herein in accordance with example embodiments. Theprogram modules may also provide various tools or techniques by whichthe computer 200 may participate within the overall systems or operatingenvironments using the components, flows, and data structures discussedthroughout this description.

In general, the program modules 214 may, when loaded into the processingunit 202 and executed, transform the processing unit 202 and the overallcomputer 200 from a general-purpose computing system into aspecial-purpose computing system. The processing unit 202 may beconstructed from any number of transistors or other discrete circuitelements, which may individually or collectively assume any number ofstates. More specifically, the processing unit 202 may operate as afinite-state machine, in response to executable instructions containedwithin the program modules 214. These computer-executable instructionsmay transform the processing unit 202 by specifying how the processingunit 202 transitions between states, thereby transforming thetransistors or other discrete hardware elements constituting theprocessing unit 202.

Encoding the program modules 214 may also transform the physicalstructure of the computer-storage media. The specific transformation ofphysical structure may depend on various factors, in differentimplementations of this description. Examples of such factors mayinclude, but are not limited to the technology used to implement thecomputer-storage media, whether the computer storage media arecharacterized as primary or secondary storage, and the like. Forexample, if the computer-storage media are implemented assemiconductor-based memory, the program modules 214 may transform thephysical state of the semiconductor memory, when the software is encodedtherein. For example, the program modules 214 may transform the state oftransistors, capacitors, or other discrete circuit elements constitutingthe semiconductor memory.

As another example, the computer-storage media may be implemented usingmagnetic or optical technology. In such implementations, the programmodules 214 may transform the physical state of magnetic or opticalmedia, when the software is encoded therein. These transformations mayinclude altering the magnetic characteristics of particular locationswithin given magnetic media. These transformations may also includealtering the physical features or characteristics of particularlocations within given optical media, to change the opticalcharacteristics of those locations. Other transformations of physicalmedia are possible without departing from the scope of the presentdescription, with the foregoing examples provided only to facilitatethis discussion.

FIG. 3 is a flow chart illustrating operations of a method 300 ofacquiring magnetic resonance imaging data, in accordance with oneexample embodiment of the present disclosure. The method 300 begins atblock 302, and according to an example embodiment, includes acquiring afirst set of spiral interleaf data for each of one or more spiral-in/outinterleaves by performing a first sampling each of one or more locationsin k-space along a first redundant spiral-in/out trajectory. At block304, the method includes acquiring a second set of spiral interleaf datafor each of the one or more spiral-in/out interleaves by performing asecond sampling of each of the one or more locations in the k-spacealong a second redundant spiral-in/out trajectory. The second redundantspiral-in/out trajectory corresponds to a time-reversed trajectory ofthe first redundant spiral-in/out trajectory. At block 306, the methodincludes combining the first set of spiral interleaf data and the secondset of spiral interleaf data with an averaging operation such as toreduce artifacts. The method 300 ends following block 306.

Spiral k-space trajectories offer many advantages over traditionalrectilinear acquisitions, including improved acquisition efficiency,less stringent hardware requirements, and natural resilience to flow andmotion [1]. However, a major hurdle to wide-spread adoption of spiraltrajectories has been their poor off-resonance performance [2]. Effortsto correct or at least mitigate the resultant blurring and distortion inspiral images in the presence of system non-idealities led to thetwo-pronged strategy of mitigation and correction in spiral imaging.

First, splitting the acquisition into multiple short interleaves reducesartifacts by ensuring that an undue amount of undesirable phase does notaccrue in a single readout. Second, much effort has been expended tocorrect for off-resonance effects in image reconstruction algorithms.These techniques vary in complexity and computational cost, from arelatively simple center frequency correction and first-order trajectorywarping method based on a least-squares fit to an acquired field-map[3], to time-[4] and frequency-segmented approaches [5], to automatic[6, 7] and semi-automatic [8] methods which demodulate the image atmultiple frequencies in order to build a composite image free ofblurring. Many of these algorithms have become large, requiring severalseconds to reconstruct a single image.

Main field inhomogeneity is a primary source of off-resonance in MRI.However, off-resonance also may be caused by other system imperfectionsbesides B₀ inhomogeneity. Particularly at lower field strengths and foroff-center slices, concomitant fields generated by normal gradientoperation may cause noticeable blur in spiral images [9]. With someexceptions [9-11], the blur due to concomitant fields has been largelyignored in the spiral literature, as it requires a more complex model toappropriately address de-blurring.

The most commonly encountered spiral trajectories are “spiral-out”. Thatis, the trajectory begins at the origin of k-space and moves outwardalong a spiral. These trajectories may be time-reversed (“spiral-in”) inorder to provide a measure of T₂*-sensitivity to the sequence [12].Combining the two, such that a spiral-out trajectory arm immediatelyfollows a spiral-in arm, results in the so-called spiral-in/outtrajectory. Although this trajectory was first proposed for efficientsampling of spin-echoes for abdominal imaging [13, 14], a version of ithas gained popularity in fMRI [15], where its SNR, speed, and resistanceto flow artifacts make it an attractive alternative to rectilinear EPImethods. Additionally, it has recently been shown to improve SNR andimage quality for real-time spiral bSSFP cardiac imaging due to itsnatural ability to center TE within TR [16].

For spiral imaging, the amount of undesired phase accrued between whenthe center of k-space is sampled and when the edge of k-space is sampleddetermines the severity of the well-known spiral blur. Given a desiredresolution, spiral-out and spiral-in/out trajectories require readoutlengths of nearly the same duration (within a few percent due todiffering amounts of time spent near the center of k-space where thek-space velocity is small). For a given readout length then, aspiral-in/out trajectory requires about half as long to move from theedge of k-space to the center compared to a spiral-out trajectory. Itfollows that for a fixed readout length and identical TE, spiral-in/outtrajectories will have better off-resonance performance than theirtraditional spiral-out counterparts.

Some embodiments of the disclosed technology may reduce or avoidblurring due to off resonance. The specific origin of off-resonance (B₀or concomitant fields) may be unimportant, as using a redundantspiral-in/out sampling scheme may naturally reduce or remove even severeoff-resonance image artifacts during image acquisition, allowing forfast and simple correction methods in the image reconstruction step.

Example Implementations and Results

The following describes examples of practicing concepts and technologiespresented herein, and corresponding results, in accordance with aspectsof the present disclosure.

Example 1 Theory

FIGS. 4A-B illustrate spiral-out and spiral-in/out read gradients,respectively. FIGS. 4C-D illustrate the k-space trajectories for thespiral out and spiral-in/out trajectories, respectively, of FIGS. 4A-B.In an example embodiment, the in/out spiral gradients may be generatedby calculating spiral-out gradients, and then time reversing thegradients (including any rewinding lobes) to act as the spiral-inportions of the trajectory. The rewinders 410 then may act as prewinders420, moving one first to the edge of k-space before data acquisitionbegins.

Conceptually, spiral-in/out trajectories may be implemented in one oftwo ways. In the first method, referred to herein as the “non-redundant”scheme, each spiral-out arm may fill in the conjugate k-space locationof the spiral-in arm, requiring the same number of interleaves as aspiral-out trajectory for equal k-space coverage. The interleaves may beincremented linearly, such that all of the spiral-in arms begin on oneedge of k-space, and all of the spiral-out arms end on the other.Alternatively, the interleaves may be interspersed such that aspiral-out arm brackets each spiral-in arm in order to disperseamplitude and phase mismatches between the two arms across the outerregions of k-space. However, severe artifacts may still occur inmulti-shot imaging when there is either a strong amplitude or phasemismatch in the data acquired with the spiral-in and spiral-out portionsof the non-redundant spiral-in/out trajectory.

The second method, referred to herein as the “redundant” scheme, mayacquire each interleaf twice, once in each direction through k-space(i.e. the redundant scheme may include acquiring two non-redundanttrajectories with the second acquisition rotated 180° in k-space). Thus,for a given resolution and field-of-view, the redundant scheme mayrequire twice the number of excitations as its non-redundantcounterpart. However, despite this prolongation of scan time, theredundant scheme may be a far more robust acquisition scheme, as eachlocation in k-space may be sampled twice: once with a spiral-in arm andonce with a spiral-out arm. The data may be then averaged, either beforeor after gridding the data onto a Cartesian matrix. Amplitude and phasemismatches between the data acquired with spiral-in and spiral-out armsof the trajectory may therefore be reduced.

To illustrate these ideas, the impact of T₂ relaxation during dataacquisition on each of the described trajectories is shown in FIG. 5.For the simulations described in this section, the number of interleaveswas 14 (28 for redundant in/out trajectory), the field of view was 300mm, and the total readout duration was 10 ms. Here, a matrix of ones wasinverse-gridded with each trajectory, T₂ relaxation on the order ofreadout length was simulated by linearly decreasing the amplitude of thesimulated data, and the simulated data was then gridded and displayed ona logarithmic scale. For spiral-out imaging, T₂ relaxation may result ina windowing of the data, with higher frequencies losing signal. Fornon-redundant spiral-in/out imaging, the appearance of the k-spaceweighting, and thus the appearance of image artifacts, may depend onwhether the interleaves are incremented linearly, or whether they aredesigned such that each spiral-in arm is bracketed by a spiral-out arm(here called interleaved-ordering). Finally, it can be seen thatredundant spiral-in/out sampling smoothes these amplitude differences,resulting in a flat frequency response. For this figure, T₂ relaxationis shown only due to the ease in visualizing magnitude differences inthe data; the theory extends to phase differences, which are discussedmore fully next.

Redundant Trajectory Response to System Non-Idealities: B₀ Off-Resonance

Point-spread-functions (PSFs) were simulated for spiral-out,non-redundant in/out, and redundant in/out trajectories, both with andwithout off-resonance (FIG. 3). PSFs were simulated by performing agridding-and-FFT reconstruction on a matrix of ones. Off-resonance wasadded by linearly increasing the phase of the simulated data. Moderateoff-resonance with spiral-out trajectories may cause a well-knownbroadening of the main PSF lobe due to undesired phase accrual duringthe spiral readout, while in non-redundant spiral-in/out, littlebroadening of the PSF main lobe may be observed However, strong ringsmay be caused by the phase mismatch (due to off-resonance) between thespiral-in and spiral-out arms. These locations of these rings may dependon the number of interleaves being used, and they may occur further awayfrom the main lobe with fewer interleaves. Redundant scanning may reduceor remove these rings through phase cancellation and leave the narrowmain lobe, resulting in an excellent PSF for spiral imaging.

To understand the origin of this effect, the signal equation of aspiral-in/out trajectory in the presence of B₀ inhomogeneity will beexamined. Ignoring relaxation, the classic demodulated signal equationin MRI is

s(t)=∫m(r)e ^(−j2πk(t)r) e ^(−jω(r)τ(t)) dr,  [1]

where m(r) is the signal, k(t) the k-space trajectory, and ω(r) theoff-resonance. For the time being, For now, let the off-resonancephase-accrual time parameter τ(t)=t, since phase accrues proportionallyto time for B₀ off-resonance. For phase accrual due to concomitantfields, τ(t) is more complex, and the concomitant field case will beaddressed in the next subsection.

It can be shown (Appendix A) that the signal resulting from theaveraging of the data from a redundant spiral-in/out trajectory is:

s(t)=∫m(r)e ^(−j2πk(t)r)[cos ω(r)t]dr.  [2]

For small-to-moderate off-resonance values, Eq. 2 shows that the signalexperiences a relatively benign cosine amplitude modulation of thesignal rather than the more serious phase modulation that arises withspiral-out trajectories in the presence of off-resonance.

FIG. 7A shows simulated normalized modulation transfer functions (MTFs)for various amounts phase accumulated by the end of the readout(corresponding to the off-resonance-time product in Eq. 2) for theredundant spiral-in/out trajectory. For redundant in/out sampling, theremay be two regimes under which the shape of the MTF may fall. In thefirst regime, the number of accumulated cycles may be small, eitherbecause there is not much off-resonance present, or because the readoutlength is short. In this regime, the cosine modulation may never reachits first zero point during the readout, so the signal may experience awindowing function which only slightly attenuates high-frequencycomponents, resulting in a slight blurring. This residual blurring maybe much less than the blurring associated with a comparable spiral-outscan. In the second regime, when the value of the off-resonance-timeproduct is high, the cosine modulation may begin nulling importantfrequencies as a function of k-space radius, resulting in imageartifacts. FIG. 7A shows the redundant spiral-in/out method will workwell as long as the number of cycles of phase remains less than 0.5. Fora 10 ms readout, this is 50 Hz. This amount of off-resonance may beeasily achieved during normal operation of clinical-strength scanners,so first-order correction may be performed on the data/trajectoriesprior to gridding in order to quickly correct gross off-resonance.

Concomitant Gradient Effects

Returning to the case where phase accrual is due to concomitant fieldeffects, it may be shown that ω_(c) (r) is a complex function of theimaging gradients and spatial coordinates of the slice, the actual formof which is unimportant for this case. As mentioned previously, in thiscase the phase-accrual time function may take a more complex form.Specifically,

$\begin{matrix}{{{\tau (t)} = {\frac{1}{g_{m}^{2}}{\int_{0}^{t}{\left\lbrack {{G_{x}^{2}\left( t^{\prime} \right)} + {G_{y}^{2}\left( t^{\prime} \right)}} \right\rbrack {t^{\prime}}}}}},} & \lbrack 3\rbrack\end{matrix}$

where g_(m) ² is the maximum gradient strength reached during the scan,and G_(x)(t′) and G_(y)(t′) are the spiral gradients on the two in-planeaxes [9]. Because this time function may depend on the gradients-squaredand because the spiral-in/out gradients are symmetric, it is easy to seethat τ(−t)=−τ(t) and the same steps of the derivation outlined inAppendix A may be followed to find that the signal in the presence ofconcomitant gradient effects is

s(t)=∫m(r)e ^(−j2πk(t)r)[cos ω_(c)(r)τ(t)]dr.  [4]

The typical phase-accrual time function for spiral gradients is,overall, less steep than the linear function that governs B₀off-resonance [11]. Thus, the redundant in/out scheme may be actuallymore robust to phase errors caused by concomitant fields than it is tothose cause by B₀ inhomogeneity, and may perform well up to about 1cycle of accrued phase (FIG. 7B).

Relaxation

Thus far, relaxation effects during the readout period have beenignored. In non-redundant multi-shot spiral-in/out scanning, T₂relaxation during the readout may result in stronger signal at one sideof the periphery of k-space than the other due to an amplitude mismatchbetween the beginning of the readout and the end (FIG. 5), the result ofwhich is artifacts that look strikingly similar to those caused byoff-resonance. By adding a T₂ decay term to Eq. 1 and assuming that thereadout time is short compared to T₂, one may arrive at the followingexpression for the signal in the presence of both off-resonance and T₂decay (see Appendix B for this derivation):

$\begin{matrix}{{s(t)} = {{\int{{m(r)}{^{{- j}\; 2\pi \; {k{(t)}}r}\left\lbrack {\cos \; {\omega (r)}t} \right\rbrack}{r}}} + {j\; {\int{{m(r)}^{{- j}\; 2\pi \; {k{(t)}}r}{\frac{t}{T_{2}(r)}\left\lbrack {\sin \; {\omega (r)}t} \right\rbrack}{{r}.}}}}}} & \lbrack 5\rbrack\end{matrix}$

This signal is complex, with a real part corresponding to the familiarcosine-modulated signal equation and an imaginary part that varies inamplitude with time. This could be potentially worrisome, since phasecancellation may be relied upon to reduce or remove off-resonanceeffects. At least two facts ameliorate the situation: First, rememberingthat time runs from −T/2 to T/2 and noting that at t=0, the imaginarycomponent drops out. It follows that, at the center of k-space where themajority of the image energy resides, there is little impact from theimaginary component of Eq. 5. Second, the ratio of t/T₂ (r) thatcontrols the amplitude of the imaginary component may always be small aslong as T₂ is larger than t_(max), which should often be the case forphysiologic relaxation values and readout lengths. However, problems mayarise in the case of gradient-echo imaging of short T₂* species.

If no off-resonance is assumed (or that off-resonance is correctedsomehow) and set ω(r)=0, it can be seen that the averaging operation inredundant sampling may work to reduce or remove T₂-induced artifacts inredundant sampling. In truth, even if the linear approximation utilizedin the derivation is relaxed (as could be necessary for a gradient-echoscan to account for T₂* decay), it is easy to visualize that inredundant sampling there may be a symmetric emphasis on the outerregions of k-space, the result of which may be more benign than theasymmetric T₂ weighting that occurs for non-redundant spiral-in/outtrajectories.

In simulations, the combination of T₂ and off-resonance may not be toodifferent from either case alone. FIG. 7C shows the performance of theredundant method in the presence of both inhomogeneity and T₂ relaxationin terms of the MTF. As expected, strong shaping of the MTF only occursfor T₂ on the order of readout length (10 ms). However, even at thisextremely short T₂, there is little degradation of the PSF (not shown).The imaginary term in Eq. 5, and thus potentially damaging phase due toT₂ relaxation, may be negligible.

To demonstrate these ideas and wrap up this subsection, FIG. 8 shows theimproved performance of the redundant in/out trajectory 880 versusspiral-out 850 and non-redundant spiral in/out trajectories 860, 870 ina numerical phantom which was first inverse-gridded, then had eithersimulated T₂ decay 820, moderate off-resonance 830, or both 840 applied,then reconstructed normally. (The row at 810 shows the control with nooff-resonance or decay.) For all parameters, the redundant in/outtrajectory may out-perform the spiral-out and non-redundant in/outtrajectories in terms of RMSE.

Though the redundant spiral-in/out trajectory may work for bothgradient-echo and spin-echo imaging, spin-echoes provide a naturalsetting in which to apply them. Since the TE of spin-echo scans isgenerally longer, the spiral-in portion of the trajectory may beinserted with little or no increase in minimum TE. Second, the in/outtrajectory may align the gradient echo generated by the spiral gradientswith the spin echo formed by the RF pulses at the center of the gradientwaveform, resulting in higher signal when the center of k-space issampled.

Simple spin-echo sequences are rarely used today, as their fasterTSE-type cousins are capable of generating similar contrast in afraction of the time. One attractive application for the redundantspiral-in/out trajectory may be a slab-selective version of the 3Dspiral TSE sequence [17]. In this sequence, multiple averages with RFchopping are used to reduce or remove spurious echo artifacts that arisefrom imperfect refocusing pulses in the echo train. Since the origins ofthe spurious echo artifacts and the spiral-in/out artifacts aredifferent, the second, redundant acquisition may be combined with theRF-chopped acquisition to acquire a fully redundant trajectory with noincrease in scan time.

Methods

A resolution phantom was scanned on a 1.5 T Siemens Avanto scanner witha gradient-echo spiral sequence with a spiral-out trajectory and aredundant spiral-in/out trajectory. Acquisition parameters were: numberof interleaves—14 (28 for spiral-in/out), spiral duration —10 ms,in-plane FOV—300 mm, slice thickness—5.0 mm. To examine off-resonanceperformance, the sequences were run once with a good shim applied, andagain with the receive frequency manually tuned 20, 40, 80, and 160 Hzoff-resonance (corresponding to 0, 0.2, 0.4, 0.8, and 1.6 cycles ofoff-resonance accumulated at the end of the readout). All images wereacquired in the transverse plane, and were gridded andFourier-transform-reconstructed with no off-resonance correction appliedin reconstruction. The gridding operation automatically sums the data atthe proper k-space locations, given the redundant trajectories.

To investigate concomitant field performance, the resolution phantom wasimaged again with both spiral-out and spiral-in/out trajectories with 14interleaves (28 for spiral-in/out), spiral duration 6.4 ms, in-plane FOV300 mm, and slice thickness 3 mm in a double-oblique orientation ((C→S−41.8°)→−27.8° near the magnet isocenter (X −9.8 mm, Y −39.6 mm, Z −21.7mm), then moved 50 mm along the z-axis (X −9.8 mm, Y −39.6 mm, Z −71.7mm) and imaged again to ensure significant concomitant fields.

To test whether the redundant trajectory can be acquired concurrent withthe second, RF-chopped average of a TSE sequence, a resolution phantomwas scanned on a 3T Siemens Trio scanner with a slab-selective 3Dstack-of-spirals TSE sequence with a spiral-out trajectory (2 averagesrequired), a spiral-in/out trajectory in which the redundant interleavesare acquired in separate chopped scans (4 averages required), and aspiral-in/out trajectory which combines the redundant interleaf scanwith the chopped scan (2 averages required). Acquisition parameterswere: spiral duration 6.4 ms, in-plane FOV 300 mm, number of slices=32,slice thickness 1.0 mm. Averages were combined after linearoff-resonance correction was applied to the k-space trajectories andafter gridding the data separately.

To test the redundant in/out trajectory in vivo, a slab-selectiveversion of the variable-flip-angle 3D spiral TSE (spiral SPACE) sequencewas used on a normal volunteer for T₂-weighted brain imaging. Scanparameters were: TR/TE 3000/200, spiral duration 6.4 ms, in-plane FOV250 mm, number of slices=64, slice thickness 1.0 mm. Forty-nineinterleaves were used for both spiral-out and spiral-in/outacquisitions. For spiral-in/out, the second, redundant interleaf scanwas combined with the chopped scan so that the total acquisition timefor both sequence variations was identical. No off-resonance correctionalgorithm was applied in reconstruction in order to better exhibit theimproved off-resonance performance of the redundant in/out sequence.

Results

The redundant spiral-in/out trajectory shows improved robustness foroff-resonance values ranging up to 0.5 cycles (FIG. 9). Above thisvalue, blurring appears and is comparable to a spiral-out scan performedwith half the amount of off-resonance applied, which is consistent withthe time elapsed between when the center and edges of k-space areacquired being half that for a spiral-in/out trajectory. Furthermore,the increase in SNR is apparent in FIG. 9 for the in/out scan due toaveraging of the redundant data.

FIG. 10 shows the spiral-out and spiral-in/out trajectories fordouble-oblique imaging planes near the magnet isocenter and off-center.The spiral-in/out trajectory results in images largely free fromblurring due to concomitant fields.

FIG. 11 shows that the redundant trajectory acquisition can be combinedwith an RF-chopped second average in slab-selective spin echo trainimaging to gain the benefits of the redundant trajectory with noincrease in scan time. One slice is shown from a 3D volume.

One slice from a 3D stack-of-spirals TSE in vivo dataset acquired withboth spiral trajectories is shown in FIG. 12. Contrast is slightlydifferent between the sequences because the spiral-out version beginsspiraling out from the k-space origin before the spin-echo has formed,whereas the spiral-in/out centers the acquisition of the center ofk-space on the spin echo. Overall, the images acquired with thespiral-in/out trajectory are sharper, and in regions of high B₀inhomogeneity, show much improved off-resonance performance.

FIG. 13 shows vessel sharpness improvement when the redundant in/outtrajectory is used for non-contrast MRA. As before, when combined withslab selection and RF chopping, this improvement is gained with noincrease in scan time.

Discussion and Conclusion

Although all of the data presented here was performed with a singlereceive channel, it is anticipated this technique will perform well inparallel imaging implementations, allowing fast reconstructions to takeplace at scan time. The complexity and reconstruction time fornon-Cartesian parallel reconstructions (which, in addition to removingnon-Cartesian aliasing artifacts, have had to address the off-resonanceissue) has been a major hurdle in their development.

For small values of off-resonance, the k-space signal in redundantsampling may experience a cosine amplitude window, which is a different(and more benign) mechanism for resolution loss compared to the PSFbroadening observed in spiral-out scanning. However, as in regularspiral imaging, this slight blurring may be space-variant depending onlocal off-resonance values. For larger off-resonance values (or for longreadout lengths), the cosine modulation may begin nulling importantfrequencies in k-space as a function of k-space radius, resulting inmore severe image artifacts. Here, it is proposed to get close to thetrue off-resonance field through an acquired field map and subsequentlinear estimation of the field. As long as the maximum deviation fromthis estimate is relatively small, the redundant spiral-in/out methodmay reduce or remove the majority of blur due to residual off-resonance.As is the case for traditional spiral-out imaging, highly inhomogeneousfields will limit redundant spiral-in/out scanning to short readoutdurations.

The fact that the redundant spiral-in/out trajectory necessarilyrequires twice the number of interleaves as a spiral-out trajectory toachieve a similar resolution cannot be overlooked. It has been shownhere that for slab-selective 3D spiral TSE imaging, at least, theredundant acquisition may be combined with the RF-chopped second averagewith no penalty in scan time. The spiral-in/out trajectory is a naturalmethod for spin-echo and TSE sequences since it aligns the gradient echowith the spin echo. For other cases where spiral trajectories areregularly used with multiple averages (e.g. fMRI, ASL), redundant in/outtrajectories can be used with no overall increase in scan time.

The redundant spiral-in/out trajectory may bear a similarity to theprevailing spiral-in/out trajectory used in fMRI, wherein the trajectoryspirals out along the same path as the spiral-in portion [18, 19].However, typically, fMRI scans are performed with few interleaves (oftensingle-shot), and the spiral-in and spiral-out data is reconstructedseparately, then adaptively combined on a pixel-by-pixel basis [18, 20].The trajectories used in fMRI then, may be redundant, but they do notadhere to the mirror-symmetry requirement of Eq. A.3. Thus, the signalequations derived in this paper may not necessarily apply in the samemanner to this class of spiral-in/out trajectory.

Appendix A

For redundant spiral-in/out trajectories, a few properties of thek-space trajectory may be defined:

tε[−T/2,T/2]  [A.1]

k ₂(t)=k ₁(−t)=−k ₁(t)  [A.2]

That is, the two trajectories are symmetric about the origin and theyare mirror images of one another. Inserting this into Eq. 1 and takingτ(t)=t, the corresponding signal equations are:

$\begin{matrix}{{s_{1}(t)} = {\int_{{- T}/2}^{T/2}{{m(r)}^{{- {j2\pi}}\; {k_{1}{(t)}}r}^{{- {{j\omega}{(r)}}}t}{r}}}} & \left\lbrack {A{.3}} \right\rbrack \\\begin{matrix}{{s_{2}\left( t^{\prime} \right)} = {\int_{{- T}/2}^{T/2}{{m(r)}^{{- j}\; 2\pi \; {k_{2}{(t^{\prime})}}r}^{{- {{j\omega}{(r)}}}t^{\prime}}{r}}}} \\{= {\int_{{- T}/2}^{T/2}{{m(r)}^{{+ {j2\pi}}\; {k_{1}{(t^{\prime})}}r}^{{- {{j\omega}{(r)}}}t^{\prime}}{r}}}}\end{matrix} & \left\lbrack {A{.4}} \right\rbrack\end{matrix}$

However, the second acquisition is run in the opposite direction throughk-space, so s₂(t) should be time-reversed. Let t=−t′.

$\begin{matrix}\begin{matrix}{{s_{2}(t)} = {\int_{{- T}/2}^{T/2}{{m(r)}^{{+ {j2\pi}}\; {k_{2}{({- t})}}r}^{{- {{j\omega}{(r)}}}{({- t})}}{r}}}} \\{= {\int_{{- T}/2}^{T/2}{{m(r)}^{{- {j2\pi}}\; {k_{1}{(t)}}r}^{{+ {{j\omega}{(r)}}}t}{r}}}}\end{matrix} & \left\lbrack {A{.5}} \right\rbrack\end{matrix}$

Finally, the signals may be combined via simple averaging.

$\begin{matrix}\begin{matrix}{{s(t)} = {\frac{1}{2}\left\lbrack {{s_{1}(t)} + {s_{2}(t)}} \right\rbrack}} \\{= {\frac{1}{2}{\int_{{- T}/2}^{T/2}{{m(r)}{^{{- {j2\pi}}\; {k_{1}{(t)}}r}\left\lbrack {^{{- j}\; \omega \; {(r)}t} + ^{{+ {{j\omega}{(r)}}}t}} \right\rbrack}{r}}}}} \\{= {\frac{1}{2}{\int_{{- T}/2}^{T/2}{{m(r)}{^{{- {j2\pi}}\; {k_{1}{(t)}}r}\left\lbrack {\cos \; {\omega (r)}t} \right\rbrack}{r}}}}}\end{matrix} & \left\lbrack {A{.6}} \right\rbrack\end{matrix}$

In all other sections of this manuscript, the integral limits [−T/2,T/2]are taken to be understood.

Appendix B

Starting again with Eqs. A.4 and A.6 and insert a T₂ decay term,

s ₁(t)=∫m(r)e ^(−j2πk) ¹ ^((t)r) e ^(−jω(r)t) e ^(−t/T) ² ^((r))dr  [B.1]

s ₂(t)=∫m(r)e ^(−j2πk) ¹ ^((t)r) e ^(+jω(r)t) e ^(+t/T) ² ^((r))dr  [B.2]

The combined signal is therefore,

s ₁(t)=½∫m(r)e ^(−j2πk) ¹ ^((t)r) [e ^(−t/T) ² ^((r)) e ^(−jω(r)t) +e^(+t/T) ² ^((r)) e ^(+jω(r)t) ]dr  [B.3]

For physiologic relaxation values and the time scales that readouts areperformed at, T₂ decay is approximately linear (for example, even asevere T₂ value of 10 ms may only result in a 13% deviation fromlinearity over a 10 ms readout). One can therefore estimate e^(t/T) ²^((r))≈1+t/T₂(r) and e^(−t/T) ² ^((r))≈1−t/T₂(r) to arrive at Eq. 5:

$\begin{matrix}\begin{matrix}{{s(t)} = {\frac{1}{2}{\int{{m(r)}{^{{- {j2\pi}}\; {k_{1}{(t)}}r}\begin{bmatrix}{{\left( {1 - {t/{T_{2}(r)}}} \right)^{{- {{j\omega}{(r)}}}t}} +} \\{\left( {1 + {t/{T_{2}(r)}}} \right)^{{+ {{j\omega}{(r)}}}t}}\end{bmatrix}}{r}}}}} \\{= {\frac{1}{2}{\int{{m(r)}{^{{- {j2\pi}}\; {k_{1}{(t)}}r}\begin{bmatrix}{\left( {^{{- {{j\omega}{(r)}}}t} + ^{{+ {{j\omega}{(r)}}}t}} \right) -} \\{\frac{t}{T_{2}(r)}\left( {^{{- {{j\omega}{(r)}}}t} - ^{{+ {{j\omega}{(r)}}}t}} \right)}\end{bmatrix}}{r}}}}} \\{= {\int{{m(r)}^{{- {j2\pi}}\; {k_{1}{(t)}}r}\left\{ {{\cos \left\lbrack {{\omega (r)}t} \right\rbrack} + {j\; \frac{t}{T_{2}(r)}{\sin \left\lbrack {{\omega (r)}t} \right\rbrack}}} \right\} {r}}}} \\{= {{\int{{m(r)}^{{- {j2\pi}}\; {k_{1}{(t)}}r}{\cos \left\lbrack {{\omega (r)}t} \right\rbrack}{r}}} +}} \\{{j\; \frac{t}{T_{2}(r)}{\int{{m(r)}^{{- {j2\pi}}\; {k_{1}{(t)}}r}{\sin \left\lbrack {{\omega (r)}t} \right\rbrack}{r}}}}}\end{matrix} & \left\lbrack {B{.4}} \right\rbrack\end{matrix}$

The specific configurations, choice of materials and chemicals, and thesize and shape of various elements can be varied according to particulardesign specifications or constraints requiring a system or methodconstructed according to the principles of the present disclosure. Forexample, while certain example ranges have been provided for the searchwindows and patch sizes, for example, other resolutions could be useddepending on the application and the desired final image resolution.Such changes are intended to be embraced within the scope of the presentdisclosure. The presently disclosed embodiments, therefore, areconsidered in all respects to be illustrative and not restrictive. Thescope of the present disclosure is indicated by the appended claims,rather than the foregoing description, and all changes that come withinthe meaning and range of equivalents thereof are intended to be embracedtherein.

LIST OF REFERENCES

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What is claimed is:
 1. A method, comprising: acquiring magneticresonance imaging (MRI) data associated with an area of interest of asubject, comprising: acquiring a first set of spiral interleaf data foreach of one or more spiral-in/out interleaves by performing a firstsampling each of one or more locations in k-space along a firstredundant spiral-in/out trajectory, acquiring a second set of spiralinterleaf data for each of the one or more spiral-in/out interleaves byperforming a second sampling of each of the one or more locations in thek-space along a second redundant spiral-in/out trajectory, wherein thesecond redundant spiral-in/out trajectory corresponds to a time-reversedtrajectory of the first redundant spiral-in/out trajectory, combiningthe first set of spiral interleaf data and the second set of spiralinterleaf data with an averaging operation such as to reduce artifacts.2. The method of claim 1, wherein the first and second redundanttrajectories are symmetric about an origin of the k-space.
 3. The methodof claim 1, wherein the first and second redundant trajectories aremirror images of one another.
 4. The method of claim 1, wherein theartifacts that are removed by the averaging operation are caused atleast by one or more of main field inhomogeneity, concomitant gradientfields and T2 decay.
 5. The method of claim 1, wherein the firstacquired spiral interleaf data is averaged before gridding the first setof acquired spiral data onto a Cartesian matrix.
 6. The method of claim1, wherein the first acquired spiral interleaf data is averaged aftergridding the first set if acquired spiral data onto a Cartesian matrix.7. The method of claim 1, wherein the number of spiral-in/outinterleaves is one.
 8. The method of claim 1, wherein acquiring the MRIdata comprises slab-selective multi-dimensional spiral turbo spin echo(TSE) sampling.
 9. A system, comprising: a magnetic resonance imaging(MRI) device; one or more processors; and at least one memory device incommunication with the MRI device, storing computer-readableinstructions that, when executed by the one or more processors, causethe system to: acquire magnetic resonance imaging (MRI) data associatedwith an area of interest of a subject, by: acquiring, by the MRI device,a first set of spiral interleaf data for each of one or morespiral-in/out interleaves by performing a first sampling each of one ormore locations in k-space along a first redundant spiral-in/outtrajectory, acquiring a second set of spiral interleaf data for each ofthe one or more spiral-in/out interleaves by performing a secondsampling of each of the one or more locations in the k-space along asecond redundant spiral-in/out trajectory, wherein the second redundantspiral-in/out trajectory corresponds to a time-reversed trajectory ofthe first redundant spiral-in/out trajectory, combining, by the one ormore processors, the first set of spiral interleaf data and the secondset of spiral interleaf data with an averaging operation such as toreduce artifacts.
 10. The system of claim 9, wherein the first andsecond redundant trajectories are symmetric about an origin of thek-space.
 11. The system of claim 9, wherein the first and secondredundant trajectories are mirror images of one another.
 12. The systemof claim 9, wherein the artifacts that are removed by the averagingoperation are caused at least by one or more of main fieldinhomogeneity, concomitant gradient fields and T2 decay.
 13. The systemof claim 9, wherein the first acquired spiral interleaf data is averagedbefore gridding the first acquired spiral data onto a Cartesian matrix.14. The system of claim 9, wherein the first acquired spiral interleafdata is averaged after gridding the first acquired spiral data onto aCartesian matrix.
 15. The system of claim 9, wherein the number ofspiral-in/out interleaves is one.
 16. The system of claim 9, whereinacquiring the MRI data comprises slab-selective multi-dimensional spiralturbo spin echo (TSE) sampling.
 17. A computer-readable storage mediumhaving stored computer-executable instructions that, when executed byone or more processors, cause a computer to perform functionscomprising: acquiring magnetic resonance imaging (MRI) data associatedwith an area of interest of a subject, comprising: acquiring a first setof spiral interleaf data for each of one or more spiral-in/outinterleaves by performing a first sampling each of one or more locationsin k-space along a first redundant spiral-in/out trajectory, acquiring asecond set of spiral interleaf data for each of the one or morespiral-in/out interleaves by performing a second sampling of each of theone or more locations in the k-space along a second redundantspiral-in/out trajectory, wherein the second redundant spiral-in/outtrajectory corresponds to a time-reversed trajectory of the firstredundant spiral-in/out trajectory, combining the first set of spiralinterleaf data and the second set of spiral interleaf data with anaveraging operation such as to reduce artifacts.
 18. Thecomputer-readable storage medium of claim 17, wherein the first andsecond redundant trajectories are symmetric about an origin of thek-space.
 19. The computer-readable storage medium of claim 17, whereinthe first and second redundant trajectories are mirror images of oneanother.
 20. The computer-readable storage medium of claim 17, whereinthe artifacts that are removed by the averaging operation are caused atleast by one or more of main field inhomogeneity, concomitant gradientfields and T2 decay.
 21. The computer-readable storage medium of claim17, wherein the first acquired spiral interleaf data is averaged beforegridding the first set of acquired spiral data onto a Cartesian matrix.22. The computer-readable storage medium of claim 17, wherein the firstacquired spiral interleaf data is averaged after gridding the first setif acquired spiral data onto a Cartesian matrix.
 23. Thecomputer-readable storage medium of claim 17, wherein the number ofspiral-in/out interleaves is one.
 24. The computer-readable storagemedium of claim 17, wherein acquiring the MRI data comprisesslab-selective multi-dimensional spiral turbo spin echo (TSE) sampling.